Capacity Fade Analysis and Model Based Optimization of Lithium-ion Batteries

Electrochemical power sources have had significant improvements in design, economy, and operating range and are expected to play a vital role in the future in a wide range of applications. The lithium-ion battery is an ideal candidate for a wide variety of applications due to its high energy/power density and operating voltage. Some limitations of existing lithium-ion battery technology include underutilization, stress-induced material damage, capacity fade, and the potential for thermal runaway. This dissertation contributes to the efforts in the modeling, simulation and optimization of lithium-ion batteries and their use in the design of better batteries for the future. While physics-based models have been widely developed and studied for these systems, the rigorous models have not been employed for parameter estimation or dynamic optimization of operating conditions. The first chapter discusses a systems engineering based approach to illustrate different critical issues possible ways to overcome them using modeling, simulation and optimization of lithium-ion batteries. The chapters 2-5, explain some of these ways to facilitate: i) capacity fade analysis of Li-ion batteries using different approaches for modeling capacity fade in lithium-ion batteries,: ii) model based optimal design in Li-ion batteries and: iii) optimum operating conditions: current profile) for lithium-ion batteries based on dynamic optimization techniques. The major outcomes of this thesis will be,: i) comparison of different types of modeling efforts that will help predict and understand capacity fade in lithium-ion batteries that will help design better batteries for the future,: ii) a methodology for the optimal design of next-generation porous electrodes for lithium-ion batteries, with spatially graded porosity distributions with improved energy efficiency and battery lifetime and: iii) optimized operating conditions of batteries for high energy and utilization efficiency, safer operation without thermal runaway and longer life

Parameter estimation of an electrochemistry-based lithium-ion battery model

The final publication is available at Elsevier via http://doi.org/10.1016/j.jpowsour.2015.04.154" © 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Parameters for an electrochemistry-based Lithium-ion battery model are estimated using the homotopy optimization approach. A high-fidelity model of the battery is presented based on chemical and electrical phenomena. Equations expressing the conservation of species and charge for the solid and electrolyte phases are combined with the kinetics of the electrodes to obtain a system of differential-algebraic equations (DAEs) governing the dynamic behavior of the battery. The presence of algebraic constraints in the governing dynamic equations makes the optimization problem challenging: a simulation is performed in each iteration of the optimization procedure to evaluate the objective function, and the initial conditions must be updated to satisfy the constraints as the parameter values change. The ε-embedding method is employed to convert the original DAEs into a singularly perturbed system of ordinary differential equations, which are then used to simulate the system efficiently. The proposed numerical procedure demonstrates excellent performance in the estimation of parameters for the Lithium-ion battery model, compared to direct methods that are either unstable or incapable of converging. The obtained results and estimated parameters demonstrate the efficacy of the proposed simulation approach and homotopy optimization procedure.The financial support of the NSERC/Toyota/Maplesoft Industrial Re-search Chair program is gratefully acknowledged

Continuum Representation for Simulating Discrete Events of Battery Operation

A mathematical approach for representing the discrete events in the cycling studies of lithium-ion batteries as a continuum event has been proposed to generate charge/discharge curves for N number of battery cycles. Simulations of up to 5000 cycles have been performed using this technique using the solid-phase diffusion model. A nonlinear electrochemical engineering model, which describes the galvanostatic charge/open-circuit/discharge processes of a thin-film nickel electrode, has also been investigated to test and validate the computational performance of the continuum representation technique. Finally, the tested technique is implemented for an existing full-order pseudo-two-dimensional lithium-ion battery model that has several coupled and nonlinear partial differential equations in multiple domains. The continuum representation, which is expressed as a function of a dependent variable in time t, works efficiently for several cycles with very minimal model initialization efforts and computation cost. However, it is not ideal for state detection. The mathematical simulation approaches that are currently followed for the modeling of charge/discharge cycles of lithium-ion batteries involve different computational schemes. 1-10 The complexity arises because of steep variations in the dependent variables ͑concentrations and potentials͒ between charge and discharge processes, difficulty in obtaining consistent initial values for the model equations, solver failure after a certain number of cycles due to high charge/discharge cutoff voltages, thermal effects, etc. We came up with a shooting method in a spatial direction 11 based on the steadystate model equations that work well for providing consistent initialization during a charge or discharge process. Wu and White 12 devised an initialization subroutine called differential algebraic equation initialization subroutine ͑DAEIS͒ to overcome numerical inconsistency and discussed in detail the initialization problems of battery models. Consistent initial values of the dependent variables for index-1 differential algebraic equation ͑DAE͒ systems can be obtained using DAEIS. DAEIS is effective in handling a DAE system with combined continuous processes and discrete events that are frequently encountered in battery operations. Before the advancement of computation capability, Tafel approximation of the electrokinetic expression and Ohm's law in electrolyte were used to calculate initial guesses for algebraic variables. 13 In this work, the complete protocol that includes many discrete events to constitute one cycle of lithium-ion battery was reformulated as a single continuous process. Then, this continuous process was repeatedly simulated up to the desired number of cycles. This was achieved by carefully changing the model variables that directly influence the cycling parameters, for example, changing the independent variable ͑in time͒ or the dependent variable ͑in solid-phase concentration at the surface of the intercalating particles͒ and expressing the same as an additional algebraic equation in terms of the number of battery cycles. This approach was attempted to overcome the difficulties mentioned during the conventional cycle studies, and it was an efficient method for many situations. Adding an additional nonlinear algebraic equation does not contribute to the significant computation cost for the model simulation; rather, it helps in effectively handling large cycle numbers and in generating the cycle data for further analysis. The proposed mathematical representation has been demonstrated for models with different degrees of complexity and in comparison with the results from those using the conventional approach. 14-16 The combination of this continuum representation and this efficient reformulated model helps in the use of meaningful models of batteries for emerging applications such as satellites, military, hybrid electric vehicles, etc. The combination of the continuum representation and the reformulated model is helpful in a way that solving the full-order physicsbased lithium-ion battery model with less computation cost was facilitated by the reformulated version of the full-order model that does not require a large system of differential and algebraic equations to be solved for each parameter in a cycle, for example, charge or discharge. Though the objective of this investigation is to devise a continuum representation for generating cycle data using a fullorder physics-based lithium-ion battery model, two other simple electrochemical models ͑mentioned above͒ are also discussed with the intention to provide more details and insight into the proposed continuum approach that can help readers to easily adopt the approach for other interesting cases

Design of Battery Electrodes with Dual‐Scale Porosity to Minimize Tortuosity and Maximize Performance

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/96689/1/1254_ftp.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/96689/2/adma_201204055_sm_suppl.pd

An optimal charging algorithm to minimise solid electrolyte interface layer in lithium-ion battery

This article presents a novel control algorithm for online optimal charging of lithium-ion battery by explicitly incorporating degradation mechanism into control, to reduce the degradation process. The health of battery directly relates to degradation and capacity fade in cycles of charging. We mainly focus on the growth of the solid electrolyte interface (SEI) layer, which is the primary source of degradation of batteries. This article addresses the challenge of minimising SEI layer growth during charging by incorporating the first-order SEI layer growth rate model into a non-linear model predictive control approach. A single particle model (SPM) is used for optimal charging using orthogonal projection-based model reformulation. Gauss pseudo-spectral method is used for the optimisation of charging trajectories. Results of the optimal algorithm are compared with the traditional constant current constant voltage (CCCV) approach without considering SEI layer growth. It is ensured that overpotential caused by lithium plating remains in a healthy regime which is another feature of the proposed strategy. Simulation results are presented to demonstrate the advantages of the proposed charging method

Optimal porosity distribution for minimized ohmic drop across a porous electrode

This paper considers the design of spatially varying porosity profiles in next-generation electrodes based on simultaneous optimization of a porous-electrode model. Model-based optimal design ͑not including the solid-phase intercalation mechanism͒ is applied to a porous positive electrode made of lithium cobalt oxide, which is commonly used in lithium-ion batteries for various applications. For a fixed amount of active material, optimal grading of the porosity across the electrode was found to decrease the ohmic resistance by 15%-33%, which in turn increases the electrode capacity to hold and deliver energy. The optimal porosity grading was predicted to have 40% lower variation in the ohmic resistance to variations in model parameters due to manufacturing imprecision or capacity fade. The results suggest that the potential for the simultaneous model-based design of electrode material properties that employ more detailed physics-based first-principles electrochemical engineering models to determine optimal design values for manufacture and experimental evaluation. © 2010 The Electrochemical Society. ͓DOI: 10.1149/1.3495992͔ All rights reserved. Electrochemical power sources have had significant improvements in design and operating range and are expected to play a vital role in the future in automobiles, power storage, military, and space applications. Lithium-ion chemistry has been identified as a preferred candidate for high-power/high-energy secondary batteries. Applications for batteries range from implantable cardiovascular defibrillators operating at 10 A current to hybrid vehicles requiring pulses of up to 100 A. Today, the design of these systems have been primarily based on ͑i͒ matching the capacity of anode and cathode materials; ͑ii͒ trial-and-error investigation of thickness, porosity, active material, and additive loading; ͑iii͒ manufacturing convenience and cost; ͑iv͒ ideal expected thermal behavior at the system level to handle high currents; and ͑v͒ detailed microscopic models to understand, optimize, and design these systems by changing one or few parameters at a time. Traditionally, macroscopic models have been used to optimize the electrode thickness or spatially uniform porosity in lithium-ion battery design. Many applications of mathematical modeling to design Li-ion batteries are available in the literature. 1-10 An approach to identify the optimal values of system parameters such as electrode thickness has been reported by Newman and co-workers. 2,5-10 Simplified models based on porous-electrode theory can provide analytical expressions to describe the discharge of rechargeable lithium-ion batteries in terms of the relevant system parameters. Newman and co-workers 2,5-8 have utilized continuum electrochemical engineering models for design and optimization as a tool for the identification of system limitations from the experimental data. Equations were developed that describe the time dependence of potential as a function of electrode porosity and thickness, the electrolyte and solid-phase conductivities, specific ampere-hour capacity, separator conductivity and thickness, and current density. Analysis of these equations yields the values of electrode porosity and electrode thickness so as to maximize the capacity for discharge to a given cutoff potential. Simplified models based on porous-electrode theory were used to describe the discharge of rechargeable lithium batteries and derive analytical expressions for the cell potential, specific energy, and average power in terms of the relevant system parameters. The resulting theoretical expressions were used for design and optimization purposes and for the identification of system limitations from experimental data. 5 Studies were performed by comparing the Ragone plots for a range of design parameters. A single curve in a Ragone plot involves hundreds of simulations wherein the applied current is varied over a wide range of magnitude. Ragone plots for different configurations are obtained by changing the design parameters ͑e.g., thickness͒ one at a time and by keeping the other parameters at constant values. This process of generating a Ragone plot is quite tedious, and typically Ragone curves reported in the literature are not smooth due to computational constraints. Batteries are typically designed only to optimize the performance at the very first cycle of operation of the battery, whereas in practice most of the battery's operation occurs under significantly degraded conditions. Further, multivariable optimization is not computationally efficient using most first-principles models described in the literature. A reformulated model Electrochemical Porous-Electrode Model Garcia et al. 14 provided a framework for modeling microstructural effects in electrochemical devices. That model can be extended to treat more complex microstructures and physical phenomena such as particle distributions, multiple electrode phase mixtures, phase transitions, complex particle shapes, and anisotropic solid-state diffusivities. As mentioned earlier, there are several treatments fo

Optimal porosity distribution for minimized ohmic drop across a porous electrode

This paper considers the design of spatially varying porosity profiles in next-generation electrodes based on simultaneous optimization of a porous-electrode model. Model-based optimal design ͑not including the solid-phase intercalation mechanism͒ is applied to a porous positive electrode made of lithium cobalt oxide, which is commonly used in lithium-ion batteries for various applications. For a fixed amount of active material, optimal grading of the porosity across the electrode was found to decrease the ohmic resistance by 15%-33%, which in turn increases the electrode capacity to hold and deliver energy. The optimal porosity grading was predicted to have 40% lower variation in the ohmic resistance to variations in model parameters due to manufacturing imprecision or capacity fade. The results suggest that the potential for the simultaneous model-based design of electrode material properties that employ more detailed physics-based first-principles electrochemical engineering models to determine optimal design values for manufacture and experimental evaluation. © 2010 The Electrochemical Society. ͓DOI: 10.1149/1.3495992͔ All rights reserved. Electrochemical power sources have had significant improvements in design and operating range and are expected to play a vital role in the future in automobiles, power storage, military, and space applications. Lithium-ion chemistry has been identified as a preferred candidate for high-power/high-energy secondary batteries. Applications for batteries range from implantable cardiovascular defibrillators operating at 10 A current to hybrid vehicles requiring pulses of up to 100 A. Today, the design of these systems have been primarily based on ͑i͒ matching the capacity of anode and cathode materials; ͑ii͒ trial-and-error investigation of thickness, porosity, active material, and additive loading; ͑iii͒ manufacturing convenience and cost; ͑iv͒ ideal expected thermal behavior at the system level to handle high currents; and ͑v͒ detailed microscopic models to understand, optimize, and design these systems by changing one or few parameters at a time. Traditionally, macroscopic models have been used to optimize the electrode thickness or spatially uniform porosity in lithium-ion battery design. Many applications of mathematical modeling to design Li-ion batteries are available in the literature. 1-10 An approach to identify the optimal values of system parameters such as electrode thickness has been reported by Newman and co-workers. 2,5-10 Simplified models based on porous-electrode theory can provide analytical expressions to describe the discharge of rechargeable lithium-ion batteries in terms of the relevant system parameters. Newman and co-workers 2,5-8 have utilized continuum electrochemical engineering models for design and optimization as a tool for the identification of system limitations from the experimental data. Equations were developed that describe the time dependence of potential as a function of electrode porosity and thickness, the electrolyte and solid-phase conductivities, specific ampere-hour capacity, separator conductivity and thickness, and current density. Analysis of these equations yields the values of electrode porosity and electrode thickness so as to maximize the capacity for discharge to a given cutoff potential. Simplified models based on porous-electrode theory were used to describe the discharge of rechargeable lithium batteries and derive analytical expressions for the cell potential, specific energy, and average power in terms of the relevant system parameters. The resulting theoretical expressions were used for design and optimization purposes and for the identification of system limitations from experimental data. 5 Studies were performed by comparing the Ragone plots for a range of design parameters. A single curve in a Ragone plot involves hundreds of simulations wherein the applied current is varied over a wide range of magnitude. Ragone plots for different configurations are obtained by changing the design parameters ͑e.g., thickness͒ one at a time and by keeping the other parameters at constant values. This process of generating a Ragone plot is quite tedious, and typically Ragone curves reported in the literature are not smooth due to computational constraints. Batteries are typically designed only to optimize the performance at the very first cycle of operation of the battery, whereas in practice most of the battery's operation occurs under significantly degraded conditions. Further, multivariable optimization is not computationally efficient using most first-principles models described in the literature. A reformulated model Electrochemical Porous-Electrode Model Garcia et al. 14 provided a framework for modeling microstructural effects in electrochemical devices. That model can be extended to treat more complex microstructures and physical phenomena such as particle distributions, multiple electrode phase mixtures, phase transitions, complex particle shapes, and anisotropic solid-state diffusivities. As mentioned earlier, there are several treatments fo

Identification and machine learning prediction of knee-point and knee-onset in capacity degradation curves of lithium-ion cells

ABSTRACT: High-performance batteries greatly benefit from accurate, early predictions of future capacity loss, to advance the management of the battery and sustain desirable application-specific performance characteristics for as long as possible. Li-ion cells exhibit a slow capacity degradation up to a knee-point, after which the degradation accelerates rapidly until the cell’s End-of-Life. Using capacity degradation data, we propose a robust method to identify the knee-point within capacity fade curves. In a new approach to knee research, we propose the concept ‘knee-onset’, marking the beginning of the nonlinear degradation, and provide a simple and robust identification mechanism for it. We link cycle life, knee-point and knee-onset, where predicting/identifying one promptly reveals the others. On data featuring continuous high C-rate cycling (1C–8C), we show that, on average, the knee-point occurs at 95% capacity under these conditions and the knee-onset at 97.1% capacity, with knee and its onset on average 108 cycles apart. After the critical identification step, we employ machine learning (ML) techniques for early prediction of the knee-point and knee-onset. Our models predict knee-point and knee-onset quantitatively with 9.4% error using only information from the first 50 cycles of the cells’ life. Our models use the knee-point predictions to classify the cells’ expected cycle lives as short, medium or long with 88–90% accuracy using only information from the first 3–5 cycles. Our accuracy levels are on par with existing literature for End-of-Life prediction (requiring information from 100-cycles), nonetheless, we address the more complex problem of knee prediction. All estimations are enriched with confidence/credibility metrics. The uncertainty regarding the ML model’s estimations is quantified through prediction intervals. These yield risk-criteria insurers and manufacturers of energy storage applications can use for battery warranties. Our classification model provides a tool for cell manufacturers to speed up the validation of cell production techniques

‘Breathing-Crystals’ The Origin of Electrochemical Activity of Mesoporous Li-MnO2

Akin to Le Chatalier’s principle, we show that a mesoporous material can mitigate the effect of stress by expanding or contracting elastically into the pore space; we simulate this ‘breathing-crystal’ phenomenon using MD simulation. In particular, our simulations reveal that mesoporous Li-MnO2 is electrochemically active because the stress, associated with charge cycling, does not influence the structure or dimensions of the (unlithiated) 1x1 tunnels in which the lithium ions intercalate and reside. Conversely, the parent bulk material suffers structural collapse and blockage of the 1x1 tunnels under stress. The mechanism associated with Li deintercalation is presented together with the activation energy barriers, which are calculated to be 0.4eV - irrespective of whether the mesoporous host is un-strained or under considerable (1.6 GPa) tensile or compressive stress

Design of 3D microbial anodes for microbial electrolysis cells (MEC) fuelled by domestic wastewater. Part I: Multiphysics modelling

The performance of a microbial electrolysis cell (MEC) supplied with domestic wastewater (dWW) is essentially limited by the kinetics of the anodic bioelectrochemical reactions and the low ionic conductivity of the electrolyte. A strategy to boost-up the anodic bioelectrochemical kinetics is to use three-dimensional (3D) microbial anodes that offer a high total anodic surface area and volume density of electroactive biofilm. In this work, a 3D multiphysics model was designed to simulate the current generation and resulting hydrogen production in double and triple-compartment MECs fed continuously with dWW. Simulations indicated that optimised 3D microbial anode geometries could simultaneously increase current and chemical oxygen demand (COD) removal by 86% compared to a 2D planar graphite electrode. At a constant CEM voltage, the current produced increased with the thickness of the 3D microbial anode up to a limiting thickness of 20 mm. Beyond this value, the current was stagnant due to the predominant ohmic drop. Current generation and COD removal could be further increased by designing 3D anode geometrical arrangements that force the dWWs to flow through the porosity of the 3D microbial anode. A gain of 20% was calculated by substituting a monolithic 3D graphite anode with a 3D anode of the same thickness (20 mm) but constructed of plates stacked on top of each other and spaced 2.5 mm apart. Finally, hydrogen production performance was additionally optimised by a further + 20% by switching from a two-compartment MEC design (anode-cathode) to a three-compartment MEC design (cathode-anode-cathode)